A new analytical method for the study of solute oxygen in biological fluids is described with reference to existing techniques. The primary method depends on the use of indirect electron spin resonance (ESR) detection by means of the effect of disolved oxygen on the linewidth of a solute nitroxide spin probe. This ESR effect is sensitive to both the concentration and diffusion coefficient of the oxygen. The theory of the effect is outlined. A unique feature of this method is that oxygen partitioned between two phases, such as a fluid bilayer membrane and the surrounding aqueous cytoplasm, can be studied simultaneously in both phases. The research plan includes optimization of the sensitivity of the ESR probe to oxygen by (1) synthesis of a per-deutero probe with reduced linewidth and (2) on-line computer deconvolution of the signals from each phase. Supplemental NMR relaxation experiments are proposed. Limitations of the techniques are discussed. It is anticipated that this technique will become an important tool in respiratory research at the molecular level.